Asteroseismic properties of solar-type stars observed with the NASA K2 mission: results from Campaigns 1-3 and prospects for future observations
Mikkel N. Lund, William J. Chaplin, Luca Casagrande, Víctor Silva Aguirre, Sarbani Basu, Allyson Bieryla, Jørgen Christensen-Dalsgaard, David W. Latham, Timothy R. White, Guy R. Davies, Daniel Huber, Lars A. Buchhave, Rasmus Handberg
AA ccepted for P ublications of the A stronomical S ociety of the P acific (PASP) Preprint typeset using L A TEX style AASTeX6 v. 1.0
ASTEROSEISMIC PROPERTIES OF SOLAR-TYPE STARS OBSERVED WITH THE NASA K2 MISSION: RESULTSFROM CAMPAIGNS 1-3 AND PROSPECTS FOR FUTURE OBSERVATIONS M ikkel N. L und (cid:63) , W illiam
J. C haplin , L uca C asagrande , V´ ictor S ilva A guirre , S arbani B asu , A llyson B ieryla ,J ørgen C hristensen -D alsgaard , D avid W. L atham , T imothy R. W hite , G uy R. D avies , D aniel H uber , L ars A. B uchhave , and R asmus H andberg (Received 2016 May 3; Revised 2016 August 9; Accepted 2016 August 22) School of Physics and Astronomy, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK Stellar Astrophysics Centre, Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, DK-8000 Aarhus C, Denmark Research School of Astronomy and Astrophysics, Mount Stromlo Observatory, The Australian National University, ACT 2611, Australia Department of Astronomy, Yale University, PO Box 208101, New Haven, CT 06520-8101, USA Harvard-Smithsonian Center for Astrophysics, 60 Garden Street Cambridge, MA 02138 USA Sydney Institute for Astronomy (SIfA), School of Physics, University of Sydney, NSW 2006, Australia SETI Institute, 189 Bernardo Avenue, Mountain View, CA 94043, USA Centre for Star and Planet Formation, Natural History Museum of Denmark & Niels Bohr Institute, University of Copenhagen, Øster Voldgade 5-7, DK-1350Copenhagen K, Denmark
AbstractWe present an asteroseismic analysis of 33 solar-type stars observed in short cadence during Campaigns (C)1-3 of the NASA K2 mission. We were able to extract both average seismic parameters and individual modefrequencies for stars with dominant frequencies up to ∼ µ Hz, and we find that data for some targets aregood enough to allow for a measurement of the rotational splitting. Modelling of the extracted parametersis performed by using grid-based methods using average parameters and individual frequencies together withspectroscopic parameters. For the target selection in C3, stars were chosen as in C1 and C2 to cover a widerange in parameter space to better understand the performance and noise characteristics. For C3 we still de-tected oscillations in 73% of the observed stars that we proposed. Future K2 campaigns hold great promise forthe study of nearby clusters and the chemical evolution and age-metallicity relation of nearby field stars in thesolar neighbourhood. We expect oscillations to be detected in ∼
388 short-cadence targets if the K2 missioncontinues until C18, which will greatly complement the ∼
500 detections of solar-like oscillations made forshort-cadence targets during the nominal
Kepler mission. For ∼ −
40 of these, including several members ofthe Hyades open cluster, we furthermore expect that inference from interferometry should be possible.
Keywords:
Asteroseismology — methods: data analysis — stars: solar-type — stars: oscillations — stars:fundamental parameters — stars: distances INTRODUCTIONThe study of solar-type stars by virtue of asteroseismol-ogy has been one of the great successes of the NASA
Kepler mission (Gilliland et al. 2010). These studies include bothensemble analysis of field stars (Chaplin et al. 2014), and in-ferences on planet hosting stars (Huber et al. 2013a; Lundet al. 2014; Van Eylen et al. 2014; Campante et al. 2015), in-cluding detailed analysis from individual mode frequencies(Silva Aguirre et al. 2015; Davies et al. 2016).The loss of a second of
Kepler ’s four reaction wheelsended the nominal mission in May of 2013. With good grace,
Kepler was expertly repurposed by the mission teams into (cid:63) [email protected] the ecliptic plane K2 mission (Howell et al. 2014). With itsobservations along the ecliptic plane K2 o ff ers a unique op-portunity to study di ff erent regions of the Galaxy. Data fromCampaign 1 (C1) have already o ff ered asteroseismic resultsof solar-like and red-giant field stars (Chaplin et al. 2015;Stello et al. 2015). From C3 onwards the operation of thefine-guidance sensors changed, resulting in a better point-ing and a significantly improved high-frequency performance(Van Cleve et al. 2016) — with the improved understandingof the data characteristics and noise properties the prospectsfor future results are promising.Compared to the nominal Kepler mission, K2 will observemany nearby bright stars, which will give us the opportunityto apply asteroseismology to study the local solar neighbour-hood, placing constraints on the age-metallicity relation ofnearby field stars. The bright targets bring powerful tests of a r X i v : . [ a s t r o - ph . S R ] S e p M ikkel N. L und et al .stellar structure and evolution to bear, because follow-up andcomplementary observations (spectroscopy, astrometry, andinterferometry) may be more readily obtained and combinedwith asteroseismology. This will also allow a better calibra-tion of seismic scaling relations, which are important to as-teroseimic ensemble studies for galactic archaeology (Miglioet al. 2013; Casagrande et al. 2014, 2016; De Silva et al.2015; Sharma et al. 2016). Moreover, K2 allows us to studymany interesting stellar clusters, which were only sparselyrepresented in the nominal
Kepler mission, especially youngclusters — these include the Hyades (Lund et al., in press),the Pleiades (White et al., in prep.), Praesepe / M44, and M67(Stello et al. in prep.), in addition to the old globular clusterM4 (Miglio et al. 2016).It is important to note that a similar view of the Galaxywill not become available with the missions coming onlinein the near future; the Transiting Exoplanet Survey Satellite(TESS; Ricker et al. 2014, 2015) will perform a near-all-skysurvey, but it will largely avoid the ecliptic. PLATO (Raueret al. 2013) will observe longer and will likely sample severaldiverse fields in its step-and-stare phase, but data will firstbecome available after 2024. For both these missions thestudy of clusters will be challenging because of the largerpixel sizes adopted.In this paper we demonstrate the utility of K2 for carryingout asteroseismic studies of field stars in the solar neighbour-hood. We find that the photometric quality of the data fromC3 is better than expected, and we detect oscillations in 73%of the observed stars that we proposed. With the extractedseismic parameters, comprising both average quantities andindividual frequencies, we are able to perform grid-based anddetailed seismic modelling.The paper is organised as follows: in Section 2 we presentthe reduction of K2 data, and the atmospheric parameters ob-tained for the targets with detected oscillations. Section 3describes the seismic parameters; Section 4 is devoted to themodelling of these, using several di ff erent pipelines. Theprospect for future K2 campaigns is the subject of Section 5,where we look at the question of noise characteristics, ourability to detect oscillations, and we assess the possibility ofcomplementary interferometric observations. We end withconcluding remarks in Section 6. DATAWe have analysed targets observed in short cadence (SC)during K2 campaigns 1-3, which were included in the guest-observer (GO) proposals 1038, 2038, and 3038 (see Table 4).In total 88 targets were selected for observation. The primaryselection criteria for the targets were based on a predicteddetectability of solar-like oscillations in the frequency rangesuited for SC observations. Another concern was to choosestars that cover a wide range in parameter space to obtain abetter understanding of the performance and noise character-istics. For details see Chaplin et al. (2015). T eff (K) l og g ( d e x ) ⊙ ⊙ ⊙ ⊙ ⊙ −0.5−0.4−0.3−0.2−0.10.00.10.20.30.40.5 [ F e / H ] ( d e x ) Figure 1 . Kiel-diagram of sample stars with detected seismic excesspower, using the grid-based model results from Section 4 (see Ta-ble 2). Stellar evolutionary tracks are calculated using GARSTECadopting [Fe / H] = The K2-Pixel-Photometry pipeline (K2P ; Lund et al.2015) was used to extract light curves from background-corrected pixel data . For the targets analysed here, all ofwhich are saturated, we defined custom pixel masks. We thencorrected the light curves for instrumental trends from the ap-parent ∼ Detecting power excess
We searched the power spectra of all observed stars in C2–3 for indications of seismic excess power; for the C1 cohortwe adopted the four targets with clearly detected oscillationsfrom Chaplin et al. (2015). We found 5 solid detectionsfor C2 targets — this yield of ∼
15% should be seen in thecontext of a very crowded field in C2 with a pointing nearthe Galactic centre, which naturally increases the noise fromaperture photometry. Also, data for both C1 and C2 weretaken before the improvement in K2 SC operations, whichtook e ff ect from C3 onwards. Six additional targets from C2did show clear oscillations, but of a classical and coherentnature rather than the stochastic nature of solar-like oscilla-tions (Aerts et al. 2010). These are all seemingly members ofthe “Upper Sco / Assoc. II Sco / Ass Sco OB 2-2” associations downloaded from the KASOC database; steroseismology with K2 3(Hoogerwerf 2000; Rizzuto et al. 2011; Luhman & Mamajek2012), and therefore possibly pre-main-sequence oscillators(Zwintz et al. 2014). The yield from C3 was, with 24 de-tections, high (73%), because of the improved pointing sta-bility. Based on the detections in C1, Chaplin et al. (2015)predicted that solar-like oscillations should be detected in C3up to ν max values of ∼ µ Hz based on an anticipated shot-noise level three times that of the nominal
Kepler missionfrom C3 onwards (Van Cleve et al. 2016). Of the targets withdetected power excess in C3 there are three with ν max abovethe solar value of ∼ µ Hz. This shows that the noiselevels are better than expected (see Section 5), and that de-tections of solar-like oscillations in main-sequence and sub-giant stars should be readily achievable with K2 SC observa-tions from C3 onwards. In Figure 1 we show a Kiel (spec-troscopic Hertzsprung-Russell) diagram (Langer & Kudritzki2014) of the stars with detected oscillations. See Table 1 forfurther information on the targets. In Figure 2 we show thefrequency-power spectra for five of the targets where individ-ual frequencies were extracted, including two of the targetswith ν max higher than the Sun. In Section 5.1 we return to thedetectability of seismic power for the targets. We note that allanalysis has been done using SC data which are a ff ected byan incorrect pixel calibration , a flaw that was recently dis-covered. The e ff ect of the incorrect calibration is largely de-pendent on the proximity of nearby bright targets that couldcontribute signal to a given target star. The time variation ofsuch a signal should correlate with the apparent movementon the CCD, hence should be corrected for in our light curvepreparation. Indeed, in comparing the power spectra fromthe recalibrated SC C3 data that was recently released withthose used in this study we found no significant improvementin the shot-noise properties. We do not expect an impact onthe measured seismic parameters in the current study fromadopting recalibrated data.2.2. Atmospheric parameters
Two sets of atmospheric parameters were obtained, onefrom spectroscopy and one from the InfraRed Flux Method(IRFM; see Casagrande et al. 2014). Below we go throughthese in turn. 2.2.1.
Spectroscopic estimates
We obtained ground-based spectroscopic data for the tar-gets in C1 and 3 from the Tillinghast Reflector Echelle Spec-trograph (TRES; Szentgyorgyi & Furész 2007; Fürész 2008)on the 1.5-m Tillinghast telescope at the F. L. Whipple Obser-vatory. The Stellar Parameter Classification pipeline (SPC;Buchhave et al. 2012) was used to derive atmospheric param-eters. Because of well-known degeneracies between spectro-scopic estimates for T e ff , log g , and [Fe / H] (Smalley 2005; see http://archive.stsci.edu/kepler/KSCI-19080-002.pdf for further details.
600 800 1000 1200 1400 1600246810
EPIC 205962429
Frequency spacing (µHz)
900 1200 1500 1800 21003691215
EPIC 206009487
Frequency spacing (µHz) P S D / B a c k g r o und EPIC 206088888
Frequency spacing (µHz)
EPIC 206245055
Frequency spacing (µHz)
Frequency (µHz)
EPIC 206064678
Frequency spacing (µHz)
Figure 2 . Background-corrected power spectra for five of the tar-gets for which individual frequencies were extracted, arranged(downwards) in order of increasing ν max and each smoothed with a ∆ ν/ µ Hz Epanechnikov filter (Epanechnikov 1969; Hastie et al.2009) — two of these have ν max values above the solar value. The in-serts show the power-of-power spectrum (PS ⊗ PS), where the mostprominent peak (marked with a red vertical line) indicated the valueof ∆ ν/
2. The vertical red lines in the main figure window indicatethe estimated ν max values (see Section 3). Torres et al. 2012) the SPC results were refined by an itera-tive procedure (Bruntt et al. 2012). Here the initial T e ff wasused together with the measured ν max to estimate the seismiclog g as g (cid:39) g (cid:12) (cid:32) ν max ν max , (cid:12) (cid:33) (cid:32) T e ff T e ff , (cid:12) (cid:33) / , (1)using ν max , (cid:12) = ± µ Hz, T e ff , (cid:12) = g (cid:12) = − (Brown et al. 1991; Kjeldsen & Bedding 1995;Huber et al. 2011; Chaplin et al. 2014). The SPC analy-sis was then re-run with log g fixed to this seismic value —convergence was generally obtained after a single iteration.We added systematic uncertainties of 59 K and 0 .
062 dex inquadrature to the T e ff and [Fe / H] estimates from SPC (see M ikkel
N. L und et al .Torres et al. 2012).2.2.2.
InfraRed Flux Method
We also estimated T e ff by means of the IRFM using broad-band JHK s photometry from the Two Micron All Sky Survey(2MASS; Cutri et al. 2003; Skrutskie et al. 2006). For targetswith detected seismic power excess the IRFM solution wasiterated against the asteroseismic surface gravity (see Equa-tion 1). In the iteration we first made a MCMC fit of the T e ff -log g solution from the IRFM evaluated at a range of log g values. Here the uncertainty on T e ff for a given log g wasobtained from the scatter between the JHK s bands. Start-ing the iteration from the spectroscopic T e ff , we evaluate theIRFM T e ff from the seismic log g (Equation 1) which is thenfed back in the iteration; the iteration is done in a MonteCarlo manner where we draw randomly from the posteriorsof the T e ff - log g fit and the solar and stellar ν max -values. Asa valuable by-product of the IRFM one obtains a measureof the stellar angular diameter, θ , which was iterated in thesame manner as T e ff . Interstellar reddening, E ( B − V ), wasincluded in the IRFM solution by adopting values from theGeneva-Copenhagen Survey (GCS; Nordström et al. 2004;Casagrande et al. 2011) if available. Otherwise, field-averagevalues of E ( B − V ) = E ( B − V ) = .
02 forC2 (which is pointed close towards the Galactic centre) wereadopted. The averages were obtained from the reddening offield stars in the GCS within ∼ ◦ of the centres of the C1,C2 and C3 pointings and beyond 40 pc in distance; for starscloser than this a zero reddening was adopted in the GCS asappropriate to the near Solar Neighbourhood (see Holmberget al. 2007). The e ff ect of reddening on the IRFM T e ff typi-cally amounts to ∼
50 K per 0 .
01 mag excess (see Casagrandeet al. 2010). To evaluate the uncertainty on T e ff due to the un-certainty in reddening we tried adopting E ( B − V ) values fromthe 3D dust map by Green et al. (2015) , derived from starsin the Pan-STARRS 1 survey. Here E ( B − V ) was taken asthe interpolated median reddening solution at the (parallax)distance of the given star. Unfortunately, most stars lie withinthe minimum distance deemed reliable by Green et al. (2015)on the grounds of low numbers of stars, and the adopted red-dening values should therefore be treated with caution. Asa systematic uncertainty we added in quadrature the di ff er-ences in T e ff and θ between this solution and the one usingfield average reddenings to the IRFM uncertainties. An addi-tional systematic uncertainty from a Monte Carlo run assign-ing photometry errors, [Fe / H] uncertainties of 0 . .
01 mag was also added. We fi-nally added zero-point uncertainties of 20 K in T e ff and 0 . θ .Three of the C2 targets (204356572, 204550630, and204926239) have uncertainties in the IFRM determination using the Python API available at http://argonaut.skymaps.info/ of T e ff in excess of 1000 K, because these targets are pos-sibly subject to high levels of reddening. The targets areindeed found to lie in close proximity to the centre of theRho Ophiuchi cloud complex. For one of these targets, EPIC204926239, we have followed a di ff erent approach than out-lined above and instead adopted the IRFM T e ff and θ solutionthat uses the E ( B − V ) from Green et al. (2015). The result-ing T e ff agrees with that obtained by Pecaut et al. (2012). InSection 4.2 we discuss the results for this target further. SEISMIC PARAMETER ESTIMATIONGlobal asteroseismic parameters ∆ ν and ν max were esti-mated for all targets with detected power excess — for theC1 targets we adopted the values presented in Chaplin et al.(2015). For all remaining stars the estimation of ν max wasachieved by fitting the stellar noise background followingLund et al. (2014). We adopted a background model givenby a sum of generalised Lorentzians with free exponents,time scales, and rms amplitudes (see Harvey 1985; Karo ff ν max was adopted to account for the power excessdue to the oscillation spectrum. A systematic fractional un-certainty of 3% on ν max was added in quadrature followingVerner et al. (2011) who found this to be the average dif-ference between di ff erent methods for estimating ν max ; themedian fractional uncertainty on ν max amounted to ∼ . ∆ ν from the peak value of the power-of-powerspectrum (PS ⊗ PS) centred on ∆ ν/
2, where the guess of ∆ ν was obtained from the ∆ ν ∝ βν α max scaling by Huber et al.(2011). The FWHM of the ∆ ν/ ∆ ν ; this gives a median fractionaluncertainty on ∆ ν of ∼ . ν max and ∆ ν values, together withthe Huber et al. (2011) scaling. As seen the measured valuesconform to the scaling relation. See Table 1 for the extracted ν max and ∆ ν values.For a select number of 8 targets we also extracted individ-ual frequencies by peak-bagging the power spectra. Moreof the targets could be peak-bagged; however, due to therelatively lower signal-to-noise ratio (SNR) of these targetsthis is beyond the scope of the current work where we sim-ply wish to assert the potential of SC observations withK2, rather than provide a full in-depth modelling of all SCtargets. The peak-bagging was performed as described inLund et al. (2014), that is, fitting a global model usingan MCMC a ffi ne invariant ensemble sampler (see Foreman-Mackey et al. 2013). Mode identification in terms of angulardegree was achieved using the (cid:15) vs. T e ff relation given inWhite et al. (2011, 2012). Figure 4 shows the échelle dia-gram (Grec et al. 1983; Bedding & Kjeldsen 2010) for EPIC206088888, for which individual frequencies could be ex-tracted (see also Figure 2).From the MCMC peak-bagging one obtains posterior dis-tributions for parameters such as the frequency splitting δν s steroseismology with K2 5
Table 1 . Parameters for the 33 target under study. For targets where the EPIC number is in boldface individual frequencies have beenextracted. “Cam.” gives the K2 campaign; “Kp” gives the
Kepler magnitude (Brown et al. 2011; Huber et al. 2015); “HIP. ID” gives the
Hipparcos identifier of the target; “ π ” gives the van Leeuwen (2007) Hipparcos parallax in milli-arc-seconds (mas); “ θ ” is the stellar angulardiameter from the IRFM in mas; “LOS” gives the line-of-sight velocity from the CfA TRES observations, corrected by − .
61 km / s. K2 Hipparcos Seismic IRFM SPCEPIC Cam. Kp HIP. ID π ν max ∆ ν θ T e ff T e ff [Fe / H] log g v sin i (cid:63) LOS(mag) (mas) ( µ Hz) ( µ Hz) (mas) (K) ( ±
77 K) ( ± .
10 dex) (cgs; ± .
10 dex) ( ± . − ) (km s − )201367296 1 7 .
439 58093 16 . ± .
88 1176 ±
58 64 . ± . . ± .
006 5746 ±
70 5740 0 .
231 4 .
015 3 .
39 19 . ± . .
440 58191 8 . ± .
02 890 ±
46 51 . ± . . ± .
003 6241 ±
77 6270 0 .
048 3 .
910 10 .
12 3 . ± . .
766 55778 8 . ± .
71 1196 ±
72 67 . ± . . ± .
003 6276 ±
117 6456 0 .
001 4 .
048 12 .
26 7 . ± . .
797 57676 12 . ± .
97 1000 ±
46 56 . ± . . ± .
005 5998 ±
134 5930 − .
036 3 .
951 4 . − . ± . .
676 81413 9 . ± .
08 1702 ±
70 84 . ± . . ± .
003 5570 ±
70 5711 0 .
390 4 .
177 3 .
21 9 . ± . .
937 80374 11 . ± .
96 1600 ±
95 79 . ± . . ± .
014 6349 ± − .
076 4 .
168 6 .
20 5 . ± . .
775 81235 9 . ± .
08 1885 ±
130 90 . ± . . ± .
010 6374 ± − .
031 4 .
241 10 . − . ± . .
506 80756 9 . ± .
10 1236 ±
80 59 . ± . . ± .
003 6336 ±
77 6370 − .
156 4 .
061 10 . − . ± . c .
039 79606 7 . ± .
42 747 ±
31 41 . ± . . ± . b ± b .
082 3 .
841 24 . − . ± . .
246 111312 13 . ± .
62 527 ±
16 33 . ± . . ± .
007 5163 ±
70 5204 − .
285 3 .
669 1 .
54 31 . ± . .
963 110537 6 . ± .
96 1084 ±
36 60 . ± . . ± .
003 6216 ±
70 6109 − .
221 3 .
988 7 .
10 32 . ± . .
333 109822 26 . ± .
53 452 ±
14 31 . ± . . ± .
015 5016 ±
70 4981 − .
261 3 .
578 0 .
95 10 . ± . a .
179 110689 11 . ± .
98 1914 ±
63 89 . ± . . ± .
003 6224 ±
70 6143 − .
044 4 .
243 12 . − . ± . .
394 110454 6 . ± .
16 692 ±
22 42 . ± . . ± .
004 5831 ±
120 5601 − .
346 3 .
781 3 . − . ± . .
972 110518 15 . ± .
62 1341 ±
59 67 . ± . . ± .
005 6451 ±
70 6443 − .
034 4 .
097 18 .
24 11 . ± . .
708 111892 16 . ± .
68 1428 ±
46 74 . ± . . ± .
004 6030 ±
70 5924 − .
213 4 .
108 3 . − . ± . .
831 109672 15 . ± .
31 3288 ±
141 138 . ± . . ± .
003 5326 ±
70 5580 0 .
309 4 .
457 1 .
62 19 . ± . .
308 108692 14 . ± .
78 1563 ±
54 74 . ± . . ± .
004 6612 ±
70 6557 − .
156 4 .
165 14 .
92 6 . ± . .
47 111534 7 . ± .
09 1550 ±
76 79 . ± . . ± .
003 6528 ±
73 6458 − .
071 4 .
161 20 .
75 6 . ± . .
033 108468 29 . ± .
74 2253 ±
76 111 . ± . . ± .
006 5861 ±
70 5818 − .
144 4 .
303 2 .
59 3 . ± . .
718 111376 10 . ± .
38 1967 ±
64 94 . ± . . ± .
003 6029 ±
70 5962 − .
036 4 .
248 3 .
74 45 . ± . .
638 110065 5 . ± .
91 1027 ±
50 55 . ± . . ± .
003 6513 ±
104 6546 0 .
013 3 .
985 27 .
42 15 . ± . .
439 110217 11 . ± .
00 2053 ±
64 95 . ± . . ± .
003 6479 ±
70 6315 − .
139 4 .
274 9 . − . ± . a .
294 110902 7 . ± .
36 861 ±
54 48 . ± . . ± .
003 6319 ±
105 6446 − .
150 3 .
903 22 .
10 18 . ± . .
824 111843 14 . ± .
81 557 ±
19 36 . ± . . ± .
007 5911 ±
104 5855 0 .
029 3 .
700 8 . − . ± . .
899 111332 16 . ± .
96 3212 ±
119 138 . ± . . ± .
003 5917 ±
70 5846 − .
375 4 .
455 2 . − . ± . .
820 109899 6 . ± .
13 972 ±
42 52 . ± . . ± .
003 6343 ±
87 6367 0 .
058 3 .
953 17 .
13 10 . ± . .
276 110002 10 . ± .
03 1252 ±
42 63 . ± . . ± .
003 6246 ±
70 6201 0 .
079 4 .
055 5 .
43 1 . ± . a .
605 109951 16 . ± .
07 3047 ±
199 137 . ± . . ± .
004 5327 ±
70 5535 − .
249 4 .
424 4 . − . ± . .
462 109836 12 . ± .
76 1060 ±
34 58 . ± . . ± .
005 5758 ±
80 5717 0 .
271 3 .
976 3 .
70 8 . ± . .
582 109783 9 . ± .
71 1218 ±
46 61 . ± . . ± .
004 6494 ±
135 6543 0 .
020 4 .
061 24 . − . ± . a .
537 110974 10 . ± .
23 895 ±
31 52 . ± . . ± .
003 6049 ±
70 6088 − .
147 3 .
910 7 .
71 15 . ± . .
749 110077 6 . ± .
00 1040 ±
39 58 . ± . . ± .
002 6471 ±
115 6605 0 .
029 3 .
991 13 . − . ± . a Double star in The Washington Double Star Catalog (WDS; Worley & Douglass 1997); b Calculated assuming an E ( B − V ) from Green et al. (2015); the obtained T e ff agrees withthat obtained by Pecaut et al. (2012); c Potential member of the Upper Scorpius association (de Zeeuw et al. 1999). ∆ ν ( µ H z )
500 1000 1500 2000 2500 3000 3500 ν max (µHz) −15−10−5051015 ∆ ν r e s i du a l ( µ H z ) Figure 3 . Top: Estimated ν max against ∆ ν ; the dashed line givesthe relation by Huber et al. (2011), with the 1 and 2 σ confidenceintervals indicated by the dark and light blue shaded regions, re-spectively. Bottom: Residual between measured ∆ ν values and thescaling relation. Frequency mod ∆ν (94.365 µHz) F r e q u e n c y ( µ H z ) l =0 l =1 l =2 Figure 4 . Échelle diagram for EPIC 206088888. The grey scaleindicate the power level going from white (low) to black (high). Themarkers indicate the extracted mode frequencies, see the legend forthe mode degree; the radial order of the l = M ikkel N. L und et al . Inclination (degrees) Sp li tt i n g ( µ H z ) Figure 5 . Correlation maps from the MCMC fits of inclination ver-sus frequency splitting for EPIC 206009487. The colour scale goesfrom low (white) to high posterior density (blue). The solid red linegives the splitting for a constant v sin i (cid:63) with corresponding uncer-tainties (dashed lines), computed from the derived stellar radius andspectroscopic v sin i (cid:63) (see Tables 1 and 2). due to rotation and the inclination angle i (cid:63) of the star (see,e. g., Chaplin et al. 2013; Huber et al. 2013b; Lund et al.2014; Davies et al. 2015). Figure 5 shows the splitting ver-sus inclination correlation map from the MCMC fit of EPIC206009487. As seen, one can recover the curved “banana-shaped” correlation indicating a constant δν s sin i (cid:63) , corre-sponding to a given projected rotational velocity v sin i (cid:63) . Inthe figure we have indicated the lines of equivalent constant δν s sin i (cid:63) from the measured spectroscopic v sin i (cid:63) (see Ta-ble 1) and modelled stellar radius (see Table 2). In additionto EPIC 206009487 we were also able to determine projectedrotation rates for EPICs 206088888 and 205962429. Thus,from ∼
80 days of K2 photometry one will in some stars be ina position to asses the stellar rotation, and possibly pin downthe inclination from time series estimates of the rotation pe-riod. SEISMIC MODELLINGIn the modelling described below results were derived us-ing the T e ff from both the SPC and the IRFM; in all cases themetallicity from the SPC was adopted. Before any modellingof individual frequencies we corrected the frequencies for theline-of-sight (LOS) velocity of the targets following Davieset al. (2014); for modelling using frequency ratios this cor-rection is insignificant. We obtained the LOS velocities fromthe Mg b order in the TRES observations, and corrected by − .
61 km / s to put the velocities onto the IAU system (seeTable 1). Most of this correction is due the fact that the CfAlibrary of synthetic spectra does not include the gravitationalredshift of the Sun. For three of the five peak-bagged targetsthe correction was at the level of the frequency uncertainties(see Figure 6). Note that the frequency shift scales linearlywith frequency, so modes above ν max will be shifted more
500 1000 1500 2000 2500 3000 3500 ν max (µHz) −0.8−0.6−0.4−0.20.00.20.40.60.8 F r e q u e n c y s h i f t @ ν m a x ( µ H z ) Figure 6 . Mode frequency shift at ν max from the line-of-sight veloc-ity of the individual targets, obtained from the SPC data. For targetswith individual frequencies from peak-bagging we have indicatedthe minimum frequency uncertainty of the five radial modes near-est ν max . For several of the targets the frequency shift exceeds theuncertainty on individual mode frequencies. than lower-frequency modes.Average seismic parameters were modelled using twopipelines: (1) The BAyesian STellar Algorithm (BASTA;Silva Aguirre et al. 2015) using evolution models calcu-lated with the Garching Stellar Evolution Code (GARSTEC;Weiss & Schlattl 2008) and frequencies computed with theAarhus adiabatic oscillation package (ADIPLS; Christensen-Dalsgaard 2008b). Besides the atmospheric observables T e ff and [Fe / H], BASTA uses the seismic quantities ∆ ν and ν max with the model ∆ ν computed from individual frequenciesand ν max computed using the usual scaling relation ( ν max ∝ g/ √ T e ff ); (2) the Yale-Birmingham code (YB; Basu et al.2010, 2012; Gai et al. 2011), which utilises three di ff erentgrids with models from the Dartmouth group (Dotter et al.2008), the Yonsei-Yale (YY) isochrones (Demarque et al.2004), and YREC2 as described by Basu et al. (2012). In YBmodel values of ∆ ν were computed using the simple scalingrelation between ∆ ν and density (i. e., ∆ ν ∝ (cid:112) M / R ), with acorrection applied to ∆ ν following White et al. (2011) to rec-tify the deviations of ∆ ν from the pure scaling. YB similarlyuse the scaling relation for ν max . For solar reference valueswe adopted ∆ ν (cid:12) = . ± . µ Hz, ν max , (cid:12) = ± µ Hz,and T e ff , (cid:12) = r and r are used rather than individ-ual frequencies directly (see Roxburgh & Vorontsov 2003;Silva Aguirre et al. 2011, 2013) — we shall refer to thisas BASTA2 to distinguish it from the use to BASTA withaverage seismic parameters; (2) the ASTEC Fitting method(ASTFIT) using evolutionary models from the Aarhus STel-lar Evolution Code (ASTEC Christensen-Dalsgaard 2008a)and frequencies from ADIPLS; (3) the Yale-Monte Carlo steroseismology with K2 7 −0.15−0.10−0.050.000.050.10 ∆ ρ / ρ YB BASTA2 ASTFIT YMCM −0.2−0.10.00.10.20.30.4 ∆ M / M −0.10−0.050.000.050.100.15 ∆ R / R
500 1000 1500 2000 2500 3000 3500 ν max (µHz) −0.9−0.6−0.30.00.30.6 ∆ t / t Figure 7 . Fractional di ff erences between results from di ff erent mod-elling pipelines, or the use of either average seismic parameters orindividual frequencies, against ν max . The comparison is relative toresults from BASTA (as (OTHER-BASTA) / BASTA, see legend for“OTHER” pipeline) using average seismic parameters and inputsfrom the IRFM (Table 2). BASTA2 indicates model results obtainedusing ratios from individual frequencies.
Method (YMCM) with evolutionary models from the YaleStellar Evolution Code (YREC; Demarque et al. 2008) andfrequencies from the code described by Antia & Basu (1994).Further details on the di ff erent codes and grids are given bySilva Aguirre et al. (2015) and Chaplin et al. (2014).4.1. Comparison of model results
In Figure 7 we show the comparison between modellingresults from di ff erent pipelines, with BASTA results fromaverage seismic parameters and IRFM inputs as the refer-ence. Overall we see a very good agreement in derived pa-rameters, with only a few examples of di ff erences exceeding1 σ . In terms of uncertainties we obtained from the BASTAgrid-based modelling formal median fractional uncertaintiesof 4 .
3% in density, 4 .
5% in mass, 2 .
4% in radius, and 17 . .
4% in den-sity, 3 .
5% in mass, 1 .
2% in radius, and 16% in age — thesample size here was notably smaller, so these median values −0.15−0.10−0.050.000.050.10 ∆ ρ / ρ BASTA
SPC - BASTA
IRFM
BASTA2
SPC - BASTA2
IRFM −0.10.00.10.2 ∆ M / M −0.08−0.040.000.040.08 ∆ R / R
500 1000 1500 2000 2500 3000 3500 ν max (µHz) −1.0−0.50.00.5 ∆ t / t Figure 8 . Fractional di ff erences between BASTA results from di ff er-ent spectroscopic inputs (see Tables 2 and 3), against ν max . BASTA2indicates model results obtained using ratios from individual fre-quencies. are statistically less secure. Concerning the use of di ff erentinput parameters we obtain for the BASTA grid-based resultsabsolute median fractional di ff erences of 0 .
7% in mass, 0 . .
2% in age, and 0 .
1% in density between usingIRFM vs. SPC input for T e ff . The comparison is shown inFigure 8. These figures agree well with those obtained fromthe YB and ASTFIT pipelines.Concerning di ff erences between pipelines we obtain forthe grid-based results from BASTA and YB median abso-lute di ff erences (relative to BASTA) of 4 .
9% in mass, 1 . .
7% in age, and 0 .
7% in density. Di ff erences inphysics between the grids used by YB and BASTA causethe YB mass or radius estimates to be larger than thoseof BASTA. Two of the three grids of models used by YBwere constructed with di ff usion, as does the BASTA gridfor M (cid:46) .
15 M (cid:12) . For models of a given mass, those withdi ff usion tend to be of lower temperature and lower lumi-nosity than those without di ff usion. This means that in agiven temperature range, models with di ff usion will have ahigher mass than models without di ff usion, causing the type M ikkel N. L und et al .of di ff erence that we see between YB and BASTA resultsbecause the masses of the stars analysed here are predomi-nately higher than 1 .
15 M (cid:12) . Since density is related to ∆ ν , ahigher mass will automatically result in a higher radius. Thethird grid of models did not include di ff usion, but since theYB results were determined from a distribution function thathad models from all three grids, the net result was somewhathigher masses.The final set of recommended parameters for our targetsample is taken from the BASTA pipeline; these can be foundin Table 2 from IRFM inputs and in Table 3 from SPC inputs.4.2. EPIC 204926239
This target was found by de Zeeuw et al. (1999) to have an84% probability of being a member of the Upper Sco associ-ation (USa). Pecaut et al. (2012) estimated an age of around11 Myr for the association. Adopting the stellar parametersestimated by Pecaut et al. (2012), with a mass of 1 . (cid:12) , thetarget would be contracting convectively as a T-Tauri star inits pre-main-sequence (PMS) phase (Marconi & Palla 1998;Aerts et al. 2010). Such a star would not reach the classi-cal instability strip where the Herbig Ae / Be stars reside, butshould oscillate in a solar-like manner from its extensive con-vective envelope (Samadi et al. 2005). While our detectionof oscillations would be exciting if the star were in its PMSphase, we find that this is likely not the case. First, if weadopt the parameters estimated by Pecaut et al. (2012) andassume the standard scaling relation for ν max extends to thePMS, a ν max -value of ∼ µ Hz is predicted — we found ν max = ± µ Hz. Secondly, T-Tauri stars are generallyfound to be very active, which should render low-amplitudesolar-like oscillations di ffi cult to observe. We find, however,only indications of low-amplitude variability that we ascribeto surface activity. All things considered, we find it unlikelythat EPIC 204926239 should be a PMS solar-like oscillator.Model grids were therefore not extended to the PMS phasein modelling this target.4.3. Seismic distances
With the seismic solution for the stellar radii and an angu-lar diameter from the IRFM, we can estimate the distance toa given target as follows: D seis = C R seis θ IRFM , (2)where C is the conversion factor to parsec (see Silva Aguirreet al. 2012; Rodrigues et al. 2014).In Figure 9 we show the comparison between seismic andparallax distances. Overall we see a good agreement in thesense that no general systematic trend is seen in the di ff er-ences with distance; from a Wilcoxon signed-rank test we We adopt 1 AU = . × km D S e i s ( p c )
25 50 75 100 125 150 175 200 225 D Hip (pc) −4−202 ( D S e i s − D H i p ) / σ Figure 9 . Top: Comparison between distances from seismology( D seis ) using grid-based results from Table 2 and from Hipparcos parallaxes ( D Hip ). Bottom: Normalised distance di ff erence (dividedby the uncertainty on the di ff erence) against Hipparcos distances.We have omitted indicating the uncertainty on the normalised dif-ference which by definition is 1 for all targets. The dashed linesshow the 1 : 1 distance relation; the dotted lines in the bottom panelindicate the 1 σ increments in the normalised di ff erences. find that the results are consistent with the null hypothesisof a symmetric distribution around zero in the di ff erences(Wilcoxon 1945; Barlow 1989). We find 14 targets with adi ff erence beyond ± σ , of these 5 have di ff erences beyond ± σ — these values are slightly larger than one would ex-pect from a normal distribution of the residuals. The reduced χ is ∼ . Kepler mission, that is, the 22targets studied in Silva Aguirre et al. (2012) for which both
Hipparcos and seismic distances were available. FUTURE K2 CAMPAIGNS5.1.
Noise and detectability
To address the question of detectability of oscillations infuture campaigns, it is essential to understand the noise char-acteristics of the observations and their relation to the a pos-teriori detectability. The targets observed in C1-3 were se-lected from the
Hipparcos catalogue under the criteria of hav-ing a relative parallax uncertainty below 15% and a ≥ ∼ µ Hz. For theseearly campaigns we deliberately sampled an extended rangeof the cool part of the HR-diagram to better determine the de-tectability in di ff erent regimes. The prediction of detectabil-ity was made using the recipe of Chaplin et al. (2011c). steroseismology with K2 9
Table 2 . Derived parameters from the seismic modelling with BASTA, with inputs from the IRFM, of the K2 targets with detected oscillationsin SC from campaigns 1-3. For the incorporation of systematic uncertainties from di ff erent pipelines and input parameters see Section 4.1 (seealso Silva Aguirre et al. 2015). “Cam.” gives the K2 campaign; “Source” indicate whether the modelling used a grid-based approach (grid) orused the individual frequencies (indv.). EPIC Cam. HIP. ID Source Mass Radius Density log g Age Distance T e ff [Fe / H](M (cid:12) ) (R (cid:12) ) (g / cm ) (cgs; dex) (Gyr) (pc) (K) (dex)201367296 1 58093 grid 1 . ± .
04 1 . ± .
04 0 . ± .
015 4 . ± .
014 6 . ± .
73 61 . ± .
94 5731 ±
65 0 . ± . . ± .
05 2 . ± .
05 0 . ± .
010 3 . ± .
013 3 . ± .
42 137 . ± .
23 6225 ± − . ± . . ± .
09 1 . ± .
05 0 . ± .
017 4 . ± .
016 4 . ± .
17 116 . ± .
14 6264 ± − . ± . . ± .
06 1 . ± .
05 0 . ± .
012 3 . ± .
014 5 . ± .
98 82 . ± .
87 6004 ± − . ± . . ± .
04 1 . ± .
03 0 . ± .
025 4 . ± .
013 11 . ± .
73 78 . ± .
25 5562 ±
71 0 . ± . · · · . ± .
04 1 . ± .
02 0 . ± .
006 4 . ± .
007 10 . ± .
65 79 . ± .
74 5575 ±
65 0 . ± . . ± .
09 1 . ± .
04 0 . ± .
025 4 . ± .
018 3 . ± .
64 80 . ± .
82 6342 ± − . ± . . ± .
08 1 . ± .
03 0 . ± .
032 4 . ± .
019 3 . ± .
67 105 . ± .
13 6342 ± − . ± . . ± .
05 1 . ± .
04 0 . ± .
012 3 . ± .
014 4 . ± .
56 107 . ± .
01 6342 ± − . ± . . ± .
07 2 . ± .
05 0 . ± .
006 3 . ± .
013 2 . ± .
41 142 . ± .
71 6238 ±
156 0 . ± . . ± .
11 2 . ± .
12 0 . ± .
005 3 . ± .
012 7 . ± .
80 67 . ± .
59 5146 ± − . ± . . ± .
03 1 . ± .
03 0 . ± .
011 3 . ± .
011 4 . ± .
41 140 . ± .
31 6160 ± − . ± . · · · . ± .
02 1 . ± .
02 0 . ± .
006 3 . ± .
006 4 . ± .
27 140 . ± .
90 6251 ± − . ± . . ± .
09 2 . ± .
12 0 . ± .
004 3 . ± .
014 10 . ± .
15 41 . ± .
20 5029 ± − . ± . . ± .
04 1 . ± .
02 0 . ± .
025 4 . ± .
012 3 . ± .
53 78 . ± .
96 6186 ± − . ± . . ± .
05 2 . ± .
06 0 . ± .
007 3 . ± .
013 5 . ± .
73 119 . ± .
38 5822 ± − . ± . . ± .
07 1 . ± .
04 0 . ± .
016 4 . ± .
013 2 . ± .
71 60 . ± .
87 6433 ± − . ± . . ± .
04 1 . ± .
03 0 . ± .
018 4 . ± .
012 6 . ± .
98 65 . ± .
92 6017 ± − . ± . · · · . ± .
04 1 . ± .
02 0 . ± .
008 4 . ± .
008 6 . ± .
86 65 . ± .
49 6030 ± − . ± . . ± .
03 0 . ± .
02 1 . ± .
062 4 . ± .
013 9 . ± .
01 50 . ± .
22 5315 ±
71 0 . ± . · · · . ± .
02 0 . ± .
01 1 . ± .
011 4 . ± .
004 7 . ± .
25 51 . ± .
96 5393 ±
52 0 . ± . . ± .
05 1 . ± .
03 0 . ± .
018 4 . ± .
011 2 . ± .
38 67 . ± .
90 6602 ± − . ± . . ± .
06 1 . ± .
04 0 . ± .
022 4 . ± .
013 2 . ± .
64 110 . ± .
73 6511 ± − . ± . . ± .
04 1 . ± .
03 0 . ± .
036 4 . ± .
011 8 . ± .
63 34 . ± .
05 5848 ± − . ± . · · · . ± .
04 1 . ± .
02 0 . ± .
012 4 . ± .
008 8 . ± .
60 34 . ± .
83 5861 ± − . ± . . ± .
05 1 . ± .
03 0 . ± .
028 4 . ± .
011 5 . ± .
10 92 . ± .
98 6017 ± − . ± . · · · . ± .
04 1 . ± .
02 0 . ± .
011 4 . ± .
007 5 . ± .
94 92 . ± .
41 6017 ± − . ± . . ± .
12 2 . ± .
07 0 . ± .
010 3 . ± .
014 2 . ± .
80 156 . ± .
58 6511 ±
97 0 . ± . . ± .
05 1 . ± .
03 0 . ± .
027 4 . ± .
011 2 . ± .
70 93 . ± .
90 6485 ± − . ± . . ± .
05 2 . ± .
05 0 . ± .
009 3 . ± .
015 3 . ± .
44 131 . ± .
02 6303 ± − . ± . . ± .
06 2 . ± .
07 0 . ± .
005 3 . ± .
013 2 . ± .
26 78 . ± .
68 5926 ± − . ± . . ± .
04 0 . ± .
02 1 . ± .
060 4 . ± .
012 5 . ± .
68 60 . ± .
77 5913 ± − . ± . · · · . ± .
04 0 . ± .
01 1 . ± .
016 4 . ± .
007 6 . ± .
65 60 . ± .
52 5913 ± − . ± . . ± .
06 2 . ± .
05 0 . ± .
009 3 . ± .
014 3 . ± .
49 150 . ± .
32 6342 ±
91 0 . ± . . ± .
09 1 . ± .
05 0 . ± .
013 4 . ± .
012 3 . ± .
88 110 . ± .
79 6251 ±
65 0 . ± . . ± .
02 0 . ± .
02 1 . ± .
084 4 . ± .
015 14 . ± .
99 45 . ± .
41 5406 ± − . ± . . ± .
05 1 . ± .
04 0 . ± .
011 3 . ± .
012 6 . ± .
77 73 . ± .
23 5757 ±
78 0 . ± . · · · . ± .
03 1 . ± .
02 0 . ± .
006 3 . ± .
006 5 . ± .
49 74 . ± .
80 5783 ±
78 0 . ± . . ± .
08 1 . ± .
05 0 . ± .
012 4 . ± .
013 2 . ± .
61 98 . ± .
38 6459 ±
117 0 . ± . . ± .
05 1 . ± .
05 0 . ± .
009 3 . ± .
012 5 . ± .
57 125 . ± .
13 6043 ± − . ± . . ± .
11 1 . ± .
06 0 . ± .
011 3 . ± .
013 3 . ± .
85 154 . ± .
61 6446 ± − . ± . NOTE : We adopt the following solar parameters: M (cid:12) = . × g; R (cid:12) = . × cm Based on the noise levels obtained for the C1 targets anal-ysed by Chaplin et al. (2015), it was predicted that oscilla-tions could be detected in 7 targets, of which 6 in the endshowed indications of oscillations — the 4 detections thatwere solid are adopted in this work. As mentioned in Sec-tion 2.1 it was anticipated from the C1 detections that solar-like oscillations should be detected up to ∼ µ Hz from C3onwards, assuming the shot noise in the time series would re-duce by a factor of ∼ . ∼ µ Hzdivided by ∼ . χ Kepler missionby Gilliland et al. (2011). The bottom left panel shows theshot-noise estimates divided by the Gilliland et al. (2011) re-0 M ikkel
N. L und et al . Table 3 . Derived parameters from the seismic modelling with BASTA, with inputs from the SPC, of the K2 targets with detected oscillationsin SC from campaigns 1-3. For the incorporation of systematic uncertainties from di ff erent pipelines and input parameters see Section 4.1 (seealso Silva Aguirre et al. 2015). “Cam.” gives the K2 campaign; “Source” indicate whether the modelling used a grid-based approach (grid) orused the individual frequencies (indv.). EPIC Cam. HIP. ID Source Mass Radius Density log g Age Distance T e ff [Fe / H](M (cid:12) ) (R (cid:12) ) (g / cm ) (cgs; dex) (Gyr) (pc) (K) (dex)201367296 1 58093 grid 1 . ± .
04 1 . ± .
04 0 . ± .
015 4 . ± .
013 6 . ± .
77 61 . ± .
90 5718 ±
71 0 . ± . . ± .
05 2 . ± .
05 0 . ± .
010 3 . ± .
013 3 . ± .
42 137 . ± .
24 6251 ± − . ± . . ± .
08 1 . ± .
05 0 . ± .
017 4 . ± .
016 3 . ± .
79 118 . ± .
24 6420 ± − . ± . . ± .
05 1 . ± .
05 0 . ± .
012 3 . ± .
014 6 . ± .
76 81 . ± .
81 5926 ± − . ± . . ± .
05 1 . ± .
03 0 . ± .
024 4 . ± .
013 8 . ± .
62 80 . ± .
40 5705 ±
78 0 . ± . · · · . ± .
05 1 . ± .
02 0 . ± .
006 4 . ± .
008 8 . ± .
53 80 . ± .
76 5718 ±
78 0 . ± . . ± .
07 1 . ± .
04 0 . ± .
024 4 . ± .
015 4 . ± .
01 80 . ± .
77 6316 ± − . ± . . ± .
04 1 . ± .
03 0 . ± .
030 4 . ± .
014 3 . ± .
54 105 . ± .
95 6199 ± − . ± . . ± .
05 1 . ± .
04 0 . ± .
012 4 . ± .
014 4 . ± .
54 107 . ± .
01 6381 ± − . ± . . ± .
05 2 . ± .
05 0 . ± .
006 3 . ± .
012 2 . ± .
26 141 . ± .
65 6225 ±
71 0 . ± . . ± .
11 2 . ± .
12 0 . ± .
005 3 . ± .
012 7 . ± .
63 68 . ± .
59 5185 ± − . ± . . ± .
04 1 . ± .
04 0 . ± .
011 3 . ± .
012 5 . ± .
63 140 . ± .
52 6082 ± − . ± . · · · . ± .
02 1 . ± .
02 0 . ± .
005 3 . ± .
004 5 . ± .
18 141 . ± .
78 6212 ± − . ± . . ± .
08 2 . ± .
11 0 . ± .
004 3 . ± .
013 11 . ± .
00 41 . ± .
04 5016 ± − . ± . . ± .
04 1 . ± .
03 0 . ± .
025 4 . ± .
012 4 . ± .
76 78 . ± .
08 6121 ± − . ± . . ± .
06 2 . ± .
06 0 . ± .
007 3 . ± .
014 6 . ± .
99 117 . ± .
36 5588 ± − . ± . . ± .
07 1 . ± .
04 0 . ± .
016 4 . ± .
013 2 . ± .
72 60 . ± .
87 6433 ± − . ± . . ± .
05 1 . ± .
04 0 . ± .
018 4 . ± .
012 7 . ± .
25 64 . ± .
02 5926 ± − . ± . · · · . ± .
05 1 . ± .
03 0 . ± .
007 4 . ± .
009 7 . ± .
21 65 . ± .
64 5939 ± − . ± . . ± .
04 0 . ± .
02 1 . ± .
060 4 . ± .
013 4 . ± .
65 52 . ± .
30 5562 ±
71 0 . ± . · · · . ± .
02 0 . ± .
01 1 . ± .
010 4 . ± .
004 4 . ± .
07 52 . ± .
97 5562 ±
65 0 . ± . . ± .
05 1 . ± .
03 0 . ± .
017 4 . ± .
011 2 . ± .
45 67 . ± .
89 6563 ± − . ± . . ± .
07 1 . ± .
04 0 . ± .
022 4 . ± .
014 3 . ± .
78 109 . ± .
71 6446 ± − . ± . . ± .
04 1 . ± .
03 0 . ± .
036 4 . ± .
012 9 . ± .
82 34 . ± .
05 5809 ± − . ± . · · · . ± .
04 1 . ± .
02 0 . ± .
012 4 . ± .
008 8 . ± .
82 34 . ± .
83 5809 ± − . ± . . ± .
06 1 . ± .
03 0 . ± .
028 4 . ± .
012 5 . ± .
36 91 . ± .
04 5965 ± − . ± . · · · . ± .
05 1 . ± .
02 0 . ± .
011 4 . ± .
008 5 . ± .
04 92 . ± .
45 5978 ± − . ± . . ± .
11 2 . ± .
07 0 . ± .
011 3 . ± .
014 2 . ± .
70 157 . ± .
60 6537 ±
78 0 . ± . . ± .
03 1 . ± .
02 0 . ± .
026 4 . ± .
010 3 . ± .
58 93 . ± .
63 6290 ± − . ± . . ± .
05 2 . ± .
05 0 . ± .
009 3 . ± .
014 3 . ± .
36 132 . ± .
17 6433 ± − . ± . . ± .
06 2 . ± .
08 0 . ± .
005 3 . ± .
013 2 . ± .
26 78 . ± .
71 5822 ± − . ± . . ± .
04 0 . ± .
02 1 . ± .
060 4 . ± .
012 7 . ± .
95 59 . ± .
76 5835 ± − . ± . · · · . ± .
04 0 . ± .
01 1 . ± .
016 4 . ± .
007 7 . ± .
94 60 . ± .
52 5848 ± − . ± . . ± .
08 2 . ± .
06 0 . ± .
009 3 . ± .
013 3 . ± .
48 151 . ± .
49 6368 ±
78 0 . ± . . ± .
08 1 . ± .
05 0 . ± .
013 4 . ± .
013 3 . ± .
97 110 . ± .
93 6212 ±
65 0 . ± . . ± .
03 0 . ± .
02 1 . ± .
083 4 . ± .
016 12 . ± .
92 45 . ± .
47 5549 ± − . ± . . ± .
04 1 . ± .
04 0 . ± .
011 3 . ± .
011 6 . ± .
80 73 . ± .
19 5718 ±
71 0 . ± . · · · . ± .
03 1 . ± .
02 0 . ± .
005 3 . ± .
006 5 . ± .
46 73 . ± .
80 5744 ±
71 0 . ± . . ± .
08 1 . ± .
05 0 . ± .
012 4 . ± .
011 2 . ± .
43 98 . ± .
33 6524 ± − . ± . . ± .
06 2 . ± .
05 0 . ± .
009 3 . ± .
012 5 . ± .
59 126 . ± .
98 6082 ± − . ± . . ± .
10 1 . ± .
06 0 . ± .
011 3 . ± .
013 2 . ± .
64 158 . ± .
85 6589 ± − . ± . NOTE : We adopt the following solar parameters: M (cid:12) = . × g; R (cid:12) = . × cm lation — from 8 (cid:46) Kp (cid:46) . Kepler mis-sion. To get an estimate of the noise
Kepler -to-K2 noise ratiowe have fitted “by-eye” a relation, given by the sum of twoexponentially decaying functions and a constant o ff set, to theratios shown in the lower left panel — this approach is su ffi -cient to enable a better prediction of the shot noise for futurecampaigns. Dividing the measured noise levels by the newnoise relation we find a small positive correlation with bore-sight distance, meaning that targets observed near the Kepler boresight are generally slightly less noisy than targets furtheraway. This was also found in Lund et al. (2015) and VanCleve et al. (2016), and can be seen as a natural consequence of the larger apparent movement of the targets on the CCDthat lie far from the boresight.To compare the current detections against expectations were-estimated the detectability of the C1-3 targets, largely us-ing the detection recipe of Chaplin et al. (2011c). We did thiswithout the use of the spectroscopically or IRFM determinedparameters in Table 1, because such estimates typically onlybecome available from follow-up observations after the fact.Hence, T e ff were estimated from broad-band colours usingthe relations of Casagrande et al. (2010). Di ff erent from theChaplin et al. (2011c) recipe we adopted the amplitude rela-tion of Huber et al. (2011), and used as the solar bolomet-ric RMS amplitude from Michel et al. (2009) of 2 . ± . steroseismology with K2 11 P Sh o t ( pp m µ H z − ) C1 C2 C3 C4 C5
Kp (mag) P Sh o t / P Sh o t , K e p l e r Boresight radial distance (degrees) P Sh o t , r a t i o / R a t i o f i t Figure 10 . Left top: Shot-noise estimates for SC targets observed during K2 campaigns 1-5, measured as the robust mean power level above8000 µ Hz. The dashed line gives the shot-noise floor from Gilliland et al. (2011). Left bottom: Shot noise divided by the Gilliland et al. (2011)noise-floor relation; the dashed line shows the relation of this ratio against magnitude — fitted “by-eye” to median binned ratios (not shown)of targets from campaigns 3-5. The dotted lines gives the dashed line times 0 . ∼
8. Right: Shot-noise ratios divided by the ratio fit from the lower left panel against the radialboresight distance in degrees. The dotted line shows the linear relation which corresponds to the estimate Pearson’s correlation between theplotted quantities. ppm . As the amplitudes in Huber et al. (2011) were esti-mated assuming a total visibility per order of c = .
04 thisvalue is also used in predicting the detectability. We used ν max , (cid:12) = ± µ Hz, and T e ff , (cid:12) = ∆ ν from ν max .Depending on the availability of JHK S magnitudes from2MASS we used (in order of preference) either the ( V − K S ),( V − H ), or ( V − J ) relation. If none of these could be used weresorted to the ( B − V ) relation. As an indicator of potentialproblems with the V -band magnitude used in the above T e ff relations we computed, if possible, also T e ff from the ( J − K )relation. Such a check is important, because the predictedvalue of ν max ultimately depends on the V -band magnitudevia the luminosity estimate (similarly, predicted angular di-ameters would be a ff ected). V and B magnitudes were ex-tracted from the Tycho2 catalogue (Høg et al. 2000), andconverted to the Johnson system using the relations in Ma-majek et al. (2002, 2006), which are based on the work byBessell (2000). For all targets we assumed a metallicity of[Fe / H] = . ± . T e ff uncertainty, and for all magni-tudes we assumed an uncertainty of ± .
02 magnitudes. Thevarious magnitudes were corrected for reddening based onthe estimate of E ( B − V ) at the (parallax) distance of a giventarget from the 3D dust map by Green et al. (2015), and us-ing extinction-to-reddening ratios ( R X ≡ A X / E ( B − V )) of R V = . ± . R K = . ± . the solar amplitude of 3 . √ R J = . ± .
1, and R H = . ± . Hipparcos parallaxes byvan Leeuwen (2007), with the bolometric correction from therelations by Flower (1996), as presented in Torres (2010).Masses were approximated from a simple mass-luminosityrelation, specifically L ∝ M ± . (see, e. g., Salaris & Cassisi2005; Malkov 2007; Eker et al. 2015).In Figure 11 we show the comparison of predicted andmeasured values of ν max , angular diameters (see Section 5.3),and T e ff for our sample. In general we see a good agreementbetween predicted and measured values. In the T e ff compar-ison one target can be identified where the ( J − K ) estimateagrees with the IRFM, but those from ( V − K S ) and ( B − V )are o ff by more than 1000 K. This likely indicates a prob-lem with the V -band magnitude and emphasises the impor-tance of the ( J − K ) sanity check of the temperature; indeedthe ν max for this target is underestimated ( ∼ µ Hz vs. ameasured value of ∼ µ Hz) from the a ff ected T e ff and lu-minosity. Two of the high ν max targets ( > µ Hz), HIP109672 and 109951, appear to be o ff in the predicted ν max .For these targets the T e ff and θ from di ff erent relations agreewith each other and with the results from the IRFM, but bothdisplay a mismatch between seismic and parallax distances(Figure 9) — this leads us to conclude that the parallax is o ff ,and that this via L a ff ects ν max . We note that HIP 109951 islisted as a double star, which might have a ff ected the parallaxdetermination.In Figure 12 we show the predicted detectabilities for theC1-3 targets. The detectability is represented by the ratio R of the predicted signal-to-noise ratio (SNR) to the thresholdSNR for a ≥
95% probability detection, using the measurednoise levels from Figure 10; for targets with a measured ν max ikkel N. L und et al . ν m a x p r e d i c t e d ( µ H z ) θ p r e d i c t e d ( m a s ) (V-K) B14 (B-V)
B14 (V-K)
K04 (B-V)
K08 T e ff p r e d i c t e d ( K ) (V-K) (V-H) (V-J) (B-V) (J-K) ν max estimated (µHz) −1000−50005001000 ∆ ν m a x ( µ H z ) θ IRFM (mas) −0.08−0.040.000.04 ∆ θ ( m a s ) T eff, IRFM (K) −600−3000300600 ∆ T e ff ( K ) Figure 11 . Comparison between predicted and estimated values for parameters of interest in predicting detectability of seismic signals and thepossibility of interferometric constraints. In each panel we have indicated the 1 : 1 line for the compared parameters and indicated the campaignwith the marker colour, where C1 is blue, C2 is green, and C3 is red. Left: Comparison between estimated and measured values of ν max forthe sample of stars with positive detections of oscillations; see the text for the order of preference for the relation for the e ff ective temperature T e ff used in deriving ν max . Middle: Comparison between angular diameters θ estimated from broad-band colours using the relations of Boyajianet al. (2014) (B14), Kervella et al. (2004) (K04), or Kervella & Fouqué (2008) (K08) and those derived from the IFRM using the seismicconstraints on log g . Right: Similar to the middle panel, but for the e ff ective temperature T e ff using di ff erent relations from Casagrande et al.(2010). If the di ff erence exceeded 600 K we truncated the di ff erence to this value, marked by the dotted line. For the two C2 targets with T e ff uncertainties > we have used that on the abscissa but the predicted value forcalculating the detectability. We see that for C3 all targetswith detected oscillations are indeed predicted to show oscil-lations. Three targets in C3 are predicted to yield no detec-tions based on their measured noise level. For two of thesewe find bright close-by targets in the downloaded pixels thatcontaminate the light curves of the primary targets; the thirdis so bright that its flux spills out of the assigned pixels. Wehave thus detected oscillations in 24 out of 30 targets wherewe should hope to make a detection based on the shot-noiselevels — this corresponds to a success rate of 80%. For theremaining 6 targets in C3 we predict detectable oscillations,but find none. Most of these targets are found to be ratheractive, with power leaking into the power spectrum from lowfrequencies — this will likely wash out the seismic signal,but not necessarily a ff ect the shot-noise levels which weremeasured from frequencies above 8000 µ Hz. In addition, ac-tivity is known to attenuate the seismic signal, which furtherdecreases the likelihood of making a detection (Chaplin et al.2011b). Activity is similarly found to be the culprit in the C2non-detections where positive detections are predicted. Allthings considered we are confident that we understand thedetectability of solar-like oscillations in K2.5.2.
Future targets
In the following we estimate the number of stars that willbe observable in future K2 campaigns and have detectable os-cillations in SC data, all of which were drawn from the
Hip-parcos catalogue. To ascertain which targets are on the de-tector we used the
K2fov tool (Mullally et al. 2016) as hosted
500 1000 1500 2000 2500 3000 3500 ν max (µHz) ℝ ≡ S N R / S N R t h r e s h o l d , % C1 C2 C3
Figure 12 . Predicted detectability against ν max . The detectability isgiven by R as the estimated SNR over the threshold for a positivedetection at the ≥
95% level, i. e., a value above 1 indicates a pre-dicted positive detection. The colours indicate the campaign of thetarget (see legend); filled markers indicate that a positive detectionwas made, vice versa for empty markers. The blue and red squaremarkers indicate the marginal detections made in C1 (Chaplin et al.2015) and C3; green crosses give the targets in C2 showing clear in-dications of Classical pulsations. Targets with a value of R > . on the website of the Kepler Asteroseismic Science Opera-tion Center (KASOC). We note that the field pointings fromC14 onwards are only approximate. For C6-8 we adoptedthe targets already selected for observations and for C10 weadopted the targets that were proposed (see Table 4). http://kasoc.phys.au.dk steroseismology with K2 13 T eff (K) l og g ( d e x ) ⊙ ⊙ ⊙ ⊙ ⊙ A g e ( G y r ) Figure 13 . Kiel-diagram of stars from K2 campaigns 11 −
18 forwhich a detection of seismic power is predicted with a probability ≥ / H] =
0, with the model age indicated via the colouralong the track. The top colour bar give the campaign of the targets.Indicated are lines of constant ν max , in increments of 250 µ Hz, andwe have specifically highlighted the iso- ν max lines at 1000, 2000,and 3000 µ Hz; the full black line gives the limit ν max at the LCnyquist frequency. The red dashed line gives the red-edge of theclassical instability strip from Pamyatnykh (2000). Fundamental parameters and predicted detectabilities wereestimated as outlined Section 5.1. We assumed a duration of80 days for all campaigns and required a detection proba-bility ≥
95% for a positive detection. We estimated the shot-noise level from the relation found in Section 5.1, but adopteda lower relative K2-to-
Kepler noise ratio of 2. Because theK2 Ecliptic Plane Input Catalog (EPIC; Huber et al. 2015) issomewhat incomplete for later campaigns we computed
Ke-pler magnitudes (Kp) following the recipe of Brown et al.(2011). Here we adopted the transformation from Tycho B T and V T to Sloan g and r , which were corrected for reddeningusing R g = . ± .
03 and R r = . ± .
03 (Yuan et al. 2013).The targets that are predicted to show detectable solar-likeoscillations are show in a Kiel-diagram in Figure 13 andlisted in Table 4. We have trimmed the sample by requir-ing that the predicted ν max should be above the LC Nyquistfrequency, and that the fractional uncertainty on the parallaxis below 15%. The total number of targets from C6-18 ap-proaches 431. If we assume a success rate of 80% then these,together with the targets analysed in the current work, willnearly match in numbers the 500 main-sequence and sub-giant solar-like oscillators known to date from Kepler (Chap-lin et al. 2011a, 2014).The yields in C4 and 5 are relatively low because thesecampaigns were devoted to the study of the Hyades, Pleiades,M44, and M67 open clusters. From Figure 10 it is evidentthat these targets are, by and large, fainter than those ob-served in C3, which decreases the detectability. Moreover, many targets in the young cluster are fast rotators which alsochallenges the detection of oscillations.In Figure 14 we show the sky positions of both current andfuture proposed targets, in galactic coordinates. As seen, K2allows for an analysis using asteroseismology of the closesolar neighbourhood. If all potential targets are eventuallyobserved we may study the chemical evolution of the solarneighbourhood and place constraints on the age-metallicityrelation of nearby field stars. A joint analysis of such a co-hort would further allow us to thoroughly test seismic scalingrelations, which are key components in, for instance, ensem-ble studies in galactic archaeology and population studies.Even better calibrations will be possible with coming Gaiaparallaxes (Perryman et al. 2001).For standard aperture photometry and reduction using,e. g., the K2P pipeline (Lund et al. 2015) it is only worthconsidering targets dimmer than Kp (cid:38) . (cid:46) .
3, but in theseproposals only for giants observed in LC. Alternatively, onemay as outlined in Pope et al. (2016) observe such bright starsindirectly from collateral smear photometry. See Table 4 forthe detection yields of current and future K2 campaigns.5.3.
Interferometry
It is interesting to look at the potential number of targetsfor which interferometry will be possible, because these tar-gets will provide a near model-independent estimate of thestellar radius when combined with
Hipparcos or Gaia paral-laxes. For this we assumed observations from the PrecisionAstronomical Visible Observations (PAVO) beam combiner(Ireland et al. 2008) at the Center for High Angular Resolu-tion Astronomy (CHARA) Array on Mt. Wilson Observa-tory, California (ten Brummelaar et al. 2005). The observingrestrictions of PAVO can largely be summarised as a declina-tion (cid:38) − ◦ , an angular diameter (cid:38) . R J -band magnitude (cid:46) Hipparcos targets on the detector in C13-18 (forC14-18 from the currently proposed pointings) we estimatedtheir angular diameters from the ( V − K ) relation of Boya-jian et al. (2014), where we adopted the 2MASS K s for the K -band magnitude. If 2MASS photometry was absent weapplied instead the ( B − V ) relation by Boyajian et al. (2014).As a cross-check we also derived the angular diameters fromthe ( V − K ) and non-linear ( B − V ) relations by Kervella et al.(2004) and Kervella & Fouqué (2008), see also Huber et al.(2012). Figure 11 shows the overall excellent agreement be-tween the estimates from these relations. To estimate the R J magnitudes we first used the relations by Brown et al. (2011)4 M ikkel N. L und et al . D cos(b) cos(l) (pc) −150−100−50050100150 D s i n ( b )( p c ) GCM44 Hyades 123456789101112131415161718 C a m p a i g n Figure 14 . Sky positions in galactic coordinates of observed targets with positive seismic detections above the LC Nyquist (filled circularmarkers), future selected and proposed targets (empty circular markers). The targets from C4 and 13 belonging to the Hyades open cluster arefurther indicated with black crosses. For C10, we assumed that the 38 proposed targets will be selected. The future proposed targets comprisethose for which we predict a positive seismic detections above the LC Nyquist. The M44 targets lack parallax distances, so these were drawnfrom a normal distribution as N (182 ,
5) pc (van Leeuwen 2009); the targets identified in M67 fall outside the plot at a distance of ∼
832 pc(Sandquist 2004) and in the approximate direction of M44. Left: Positions of targets in galactic longitude ( l ), latitude ( b ), and distance ( D )from the Sun. The di ff erent colours indicate the K2 campaign (see colour bar in right panel). For C9, where no targets were proposed, we haveindicated the direction with the coloured line. The galactic centre (GC) is in the direction of l = ◦ . Right: Positions projected in the abscissaonto the l = ◦ → ◦ line, with the direction of the GC to the right. The colour bar indicates the colour adopted for a given K2 campaign. R (mag) θ ( m a s ) × Hyades C11C12 C13C14 C15C16 C17C18 ν m a x ( µ H z ) Figure 15 . Estimated angular diameters against R -band magnitudesfor targets in C13-18 for which we anticipate detections of seismicexcess power. All targets have declinations above − ◦ , and no re-strictions were put on parallax precision. The dotted lines indicatethe approximate limits for sensible interferometric constraints fromPAVO, hence targets fulfilling both constraints are found in the up-per left quadrant. The colours indicate the predicted ν max value,where targets with ν max below (above) the LC Nyquist are given inblue (red). Red targets should thus be observed in SC. Note thatthe ν max range covered by the two partitions di ff er by more than anorder of magnitude. For targets that are only half filled we predict aratio 0 . < R <
1. Targets that according to Perryman et al. (1998)belongs to the Hyades open cluster are marked by crosses. to convert Tycho B T and V T to analogues of Sloan g and r —we then used the R J ( g, r ) relation by Lupton (2005) . The R J band estimate was finally de-reddened using R R = . ± . E ( B − V ) from Green et al. (2015) asdetermined in Section 5.1.In Figure 15 we show the targets from C13-18 with adeclination above − ◦ that should show detectable oscilla-tions, and with potential for interferometric inference. Tar-gets rendered in blue are predicted to have ν max below the LCNyquist frequency and vice versa for targets in red, whichwith ν max > µ Hz should be observed in SC mode. Wefind of the order ∼ −
40 SC targets that will be suited forboth asteroseismic and interferometric analysis. From Perry-man et al. (1998) several of these belong to the Hyades opencluster. An asteroseismic ensemble study of these, combinedwith independent constraints on radius from interferometry,would allow for tighter constraints to be put on the clusterdistance and age. For an analysis of Hyades targets observedby K2 in C4 we refer to Lund et al. (2016, in press). More-over, for the brightest targets in the sample we will havethe possibility of conducting contemporaneous observationswith the telescope of the Stellar Observations Network Group http://classic.sdss.org/dr5/algorithms/sdssUBVRITransform.html steroseismology with K2 15
Table 4 . Overview of the number of targets observed or proposedin di ff erent campaigns together with the number of detections made.The parentheses in the “targets” column indicate that the values areour projected estimate of the number of targets that should show de-tectable oscillations. The values in parentheses in the “detections”indicate the projected yield, where we have assumed an 80% suc-cess rate. On the bottom-line the values in parentheses include bothtargets from observed campaigns and those that are either selectedor in the future. Cam. † PI †† Notes S e l ec t e d / Pleiades5 51 12 5074 Basu Praesepe / M676 35 (28) 6039 Davies North Galactic cap7 34 (27) 7039 Davies Near galactic centre8 41 (33) 8002 Campante P r opo s e d F u t u r e
14 (32) (25)15 (29) (23)16 (22) (17)17 (56) (44) North Galactic cap18 (19) (15)281 (602) 47 (388) † Proposal ID within the K2 Guest Observer (GO) program; †† Principal Investigator (SONG; Grundahl et al. 2009, 2014). CONCLUSIONWe have presented an asteroseismic analysis of 33 solar-like oscillators from SC observations during K2 campaigns1-3. We find that the quality of the data from C3 onwards issu ffi cient for extraction of seismic parameters, and in addi-tion to the average parameters ∆ ν and ν max one can peak-bagthe frequency power spectra to recover individual frequen-cies. In terms of noise we find this to be better than whatcould have been hoped for, allowing us to detect oscillationsbeyond the solar ν max .Modelling was performed using di ff erent pipelines. Theagreement between the values returned from these was ex-cellent and only in a few cases beyond the uncertainties fromthe individual pipelines. For the grid-based pipelines theseindividual uncertainties were not significantly di ff erent fromwhat could be obtained in the nominal Kepler mission, be-cause the uncertainty on ν max and ∆ ν is relatively insensitiveto the duration of the observations. For individual frequen-cies the precision naturally improves with observing length,but for modes that are well resolved compared to the modeline width one may still obtain individual frequencies that aresu ffi ciently precise for modelling.Concerning the comparison between seismic and parallaxdistances we see from Figure 9 that the dominant uncertaintyis on the Hipparcos distances. If one assumes an uncertainty on the parallax of ∼ µ as , which will likely be achievedfrom the Gaia mission (Michalik et al. 2015) for the param-eter range of the sample, such a comparison would providea strong test of the results from seismic modelling and a bet-ter assessment of potential systematic di ff erences. With anassumed parallax uncertainty of ∼ µ as, the dominant un-certainty in the comparison will shift to the other quantitiesneeded to derive seismic distances, i. e., the seismic radii wewish to test and / or the uncertainties intrinsic to bolometriccorrection and angular diameter determinations.With K2 the possibility for obtaining independent radiimeasurements from interferometry is significantly improved,because the targets under study for solar-like oscillations aretypically brighter than in the nominal Kepler mission. In Sec-tion 5.3 we found that several targets in C13-18, includingmembers of the Hyades open cluster, will be apt for interfer-ometric analysis. Because of the brightness of these targetswe may further conduct contemporaneous observations withSONG — a combined asteroseismic analysis of both the pho-tometric light curve from K2 and the RV data from SONGwould allow for a very detailed characterisation of a givenstar.Comparing the detections made for C3 targets with expec-tations we achieved a 80% success rate. We are thereforeconfident that we understand the noise characteristics in K2,and with the updated prescription for the shot noise we arein a good position to propose targets for SC observations infuture campaigns. Campaigns 13 and 18 are especially inter-esting because we may here complement the seismic analysiswith interferometry, and several members of the Hyades arepredicted to show detectable oscillations. We project that bythe end of C18 (if selected) we shall have of the order 388targets for which a seismic analysis can be accomplished.From these we may calibrate seismic scaling relations, es-pecially using the targets with independent constraints frominterferometry or precise parallaxes. This is essential to seis-mic galactic archaeology studies, which rely on such scal-ing relations. While Gaia will become important for suchcalibrations there is a strong reciprocity, because the resultsfrom our asteroseismic analysis can be used to calibrate theGaia stellar classification pipeline — something that has al-ready been requested by the Gaia team. With the samplingalong the ecliptic these will allow us to study chemical evolu-tion of the solar neighbourhood and place constraints on theage-metallicity relation of nearby field stars. The inferencesdrawn from K2 will further complement those from TESS,whose observing fields in the baseline mission largely missthe ecliptic.
Funding for this Discovery mission is provided by NASA’s Science Mis-sion Directorate. The authors acknowledge the dedicated team behind ikkel N. L und et al . the Kepler and K2 missions, without whom this work would not havebeen possible. M.N.L. acknowledges the support of The Danish Coun-cil for Independent Research | Natural Science (Grant DFF-4181-00415).M.N.L. was partly supported by the European Community’s Seventh Frame-work Programme (FP7 / Kepler )funded by the European Research Council (Grant agreement no.: 267864).W.J.C. and G.R.D acknowledge the support of the UK Science and Tech-nology Facilities Council (STFC). V.S.A. and T.R.W. acknowledges supportfrom VILLUM FONDEN (research grant 10118). S.B. acknowledges par-tial support of NASA grant NNX13AE70G and NSF grant AST-1514676. D.W.L. acknowledges partial support from the
Kepler mission via Cooper-ative Agreement NNX13AB58A with the Smithsonian Astrophysical Ob-servatory. D.H. acknowledges support by the Australian Research Coun-cil’s Discovery Projects funding scheme (project number DE140101364)and support by the NASA grant NNX14AB92G issued through the Ke-pler Participating Scientist Program. This research made use of Astropy,a community-developed core Python package for Astronomy (Astropy Col-laboration, 2013). This research has made use of the SIMBAD database andVizieR access tool, operated at CDS, Strasbourg, France. This publicationmakes use of data products from the Two Micron All Sky Survey, which isa joint project of the University of Massachusetts and the Infrared Process-ing and Analysis Center / California Institute of Technology, funded by theNational Aeronautics and Space Administration and the National ScienceFoundation.
REFERENCES
Aerts, C., Christensen-Dalsgaard, J., & Kurtz, D. W. 2010,Asteroseismology, Astronomy and Astrophysics Library (SpringerNetherlands), doi:10.1007 / / / SOHO 21, ed. M. Dikpati, T. Arentoft,I. González Hernández, C. Lindsey, & F. Hill, 579Grundahl, F., Christensen-Dalsgaard, J., Pallé, P. L., et al. 2014, in IAUSymposium, Vol. 301, IAU Symposium, ed. J. A. Guzik, W. J. Chaplin,G. Handler, & A. Pigulski, 69–75Handberg, R., & Lund, M. N. 2014, MNRAS, 445, 2698Harvey, J. 1985, in ESA Special Publication, Vol. 235, Future Missions inSolar, Heliospheric & Space Plasma Physics, ed. E. Rolfe & B. Battrick,199–208Hastie, T., Tibshirani, R., & Friedman, J. 2009, The Elements of StatisticalLearning: Data Mining, Inference, and Prediction, Second Edition,Springer Series in Statistics (Springer Science & Business Media)Høg, E., Fabricius, C., Makarov, V. V., et al. 2000, A&A, 355, L27Holmberg, J., Nordström, B., & Andersen, J. 2007, A&A, 475, 519Hoogerwerf, R. 2000, MNRAS, 313, 43Howell, S. B., Sobeck, C., Haas, M., et al. 2014, PASP, 126, 398Huber, D., Bryson, S. T., Haas, M. R., et al. 2015, ArXiv e-prints,arXiv:1512.02643Huber, D., Bedding, T. R., Stello, D., et al. 2011, ApJ, 743, 143Huber, D., Ireland, M. J., Bedding, T. R., et al. 2012, ApJ, 760, 32Huber, D., Chaplin, W. J., Christensen-Dalsgaard, J., et al. 2013a, ApJ, 767,127Huber, D., Carter, J. A., Barbieri, M., et al. 2013b, Science, 342, 331Ireland, M. J., Mérand, A., ten Brummelaar, T. A., et al. 2008, in SPIEConference Series, Vol. 7013, Optical and Infrared Interferometry,701324Kallinger, T., De Ridder, J., Hekker, S., et al. 2014, A&A, 570, A41Karo ff , C. 2012, MNRAS, 421, 3170Kervella, P., & Fouqué, P. 2008, A&A, 491, 855Kervella, P., Thévenin, F., Di Folco, E., & Ségransan, D. 2004, A&A, 426,297Kjeldsen, H. 1992, PhD thesis, University of Aarhus, Denmark, (1992)Kjeldsen, H., & Bedding, T. R. 1995, A&A, 293, 87Langer, N., & Kudritzki, R. P. 2014, A&A, 564, A52Lomb, N. R. 1976, Ap&SS, 39, 447 steroseismology with K2 17
Luhman, K. L., & Mamajek, E. E. 2012, ApJ, 758, 31Lund, M. N., Handberg, R., Davies, G. R., Chaplin, W. J., & Jones, C. D.2015, ApJ, 806, 30Lund, M. N., Lundkvist, M., Silva Aguirre, V., et al. 2014, A&A, 570, A54Malkov, O. Y. 2007, MNRAS, 382, 1073Mamajek, E. E., Meyer, M. R., & Liebert, J. 2002, AJ, 124, 1670—. 2006, AJ, 131, 2360Marconi, M., & Palla, F. 1998, ApJL, 507, L141Michalik, D., Lindegren, L., & Hobbs, D. 2015, A&A, 574, A115Michel, E., Samadi, R., Baudin, F., et al. 2009, A&A, 495, 979Miglio, A., Chiappini, C., Morel, T., et al. 2013, MNRAS, 429, 423Miglio, A., Chaplin, W. J., Brogaard, K., et al. 2016, MNRAS, 461, 760Mullally, F., Barclay, T., & Barentsen, T. 2016, K2fov: v3.0.1,doi:10.5281 / zenodo.44283Nordström, B., Mayor, M., Andersen, J., et al. 2004, A&A, 418, 989Pamyatnykh, A. A. 2000, in ASP Conf. Ser, Vol. 210, Delta Scuti andRelated Stars, ed. M. Breger & M. Montgomery, 215Pecaut, M. J., Mamajek, E. E., & Bubar, E. J. 2012, ApJ, 746, 154Perryman, M. A. C., Brown, A. G. A., Lebreton, Y., et al. 1998, A&A, 331,81Perryman, M. A. C., de Boer, K. S., Gilmore, G., et al. 2001, A&A, 369,339Pope, B. J. S., White, T. R., Huber, D., et al. 2016, MNRAS, 455, L36Rauer, H., Catala, C., Aerts, C., et al. 2013, ArXiv e-prints,arXiv:1310.0696Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2014, in Society ofPhoto-Optical Instrumentation Engineers (SPIE) Conference Series, Vol.9143, Society of Photo-Optical Instrumentation Engineers (SPIE)Conference Series, 20Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, JATIS, 1, 014003Rizzuto, A. C., Ireland, M. J., & Robertson, J. G. 2011, MNRAS, 416, 3108Rodrigues, T. S., Girardi, L., Miglio, A., et al. 2014, MNRAS, 445, 2758Roxburgh, I. W., & Vorontsov, S. V. 2003, A&A, 411, 215Salaris, M., & Cassisi, S. 2005, Evolution of Stars and Stellar Populations(The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ,England: John Wiley & Sons, Ltd), doi:10.1002 / //